A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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  1. Horse pregnancies. Bigger animals tend to carry their young longer before birth. The length of horse pregnancies from conception to birth varies according to a roughly normal distribution with a mean of 336 days and a standard deviation of 6 days. 

 

  1.  Sketch a graph of the distribution of lengths of horse pregnancies. Label the mean and the points that are 1, 2, and 3 standard deviations from the mean. 

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  1. Use the 68-95-99.7 rule to estimate the percentage of horse pregnancies that are no longer than 342 days. 
Expert Solution
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Step 1

68-95-99.7 rule

According to 68-95-99.7 rule , 

1) 68% of data falls within the first standard deviation from the mean
In mathematical notation, this is represented as: μ ± 1σ 

2) 95% fall within two standard deviations
In mathematical notation, this is represented as: μ ± 2σ

3) 99.7% fall within three standard deviations.
In mathematical notation, this is represented as: μ ± 3σ

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